Antifriction worm drive



July 23, 1946. H. s. HOFFAR 2,404,373

ANTIFRICTION WORM DRIVE Filed Aug. 1, 1 944 2 Shets-Sheet 1 INVENTOR. Henry S. Hoffar ATTORNEYS Jul 23, 1946; H a H FA 2,404,378

ANTIFRICTION WORM DRIVE Filed Aug. 1. 1944 I 2 Sheets-Sheet 2 4 6 8 .ar Angle-Dayna mm 1.5 90 45 o 45 9o 5 I 0 Warm Angle-Degrees Jig. 6

INVENTORL' Y Henry 5. Hoffar v BY I 4W ATTORNEYS Patented July 23, 1946 ANTIERICTION WORM DRIVE Henry S. Hoflfar, Vancouver. British Columbia, Canada, assignor to The Cleveland Pneumatic Tool Company, Cleveland, Ohio, a corporation of Ohio Application August 1, 1944, Serial No. 547,579

This invention pertains to antifriction worm drive mechanism, particularly that type which is adapted for incorporation in automotive steering gears. 7

It has been proposed heretofore, in an antifriction worm drive, to utilize a cylindrical worm about which bearing balls circulate, and which balls engage complemental grooves of a gear sector. Such antifriction worm and gear mechanism is shown, for example, in Figures '7 and 8 of my patent application SerialNo. 517,927, filed Jan. 12, 1944. In that instance the balls in only a single row engage the worm gear or sector at any given time.

It has further been proposed, as illustrated in Figures 11 and 12 of my aforesaid patent application, for example, to utilize in such a combination a, worm having a central portion of smaller size than its end portions, so that the concavity of its periphery inan axial plane would correspond to the peripheral convexity of the worm gear or sector in a plane perpendicular to its axis. In such an arrangement at least two, and at times perhaps three, rows of balls would be interengaged between the worm and gear.

The principal advantage of using an antifriction worm and gear combination is the increased efliciency of the drive resulting from the reduction in friction. Minimum drag can only be obtained if all sliding friction between the worm and gear or gear sector is eliminated, and only rolling friction is present. In a concave type of worm, therefore, such as disclosed in Figures 11 and 12 of my aforesaid application, maximum efiiciency is not obtained because sliding friction is not completely eliminated.

Although the balls midway between the ends of such a concave worm, which are closest to its axis of rotation, must move along the worm groove at the same speed as the balls nearer one end of the worm, and hence farther from its axis of rotation, the peripheral velocity ofthe worm portion engaging balls farther from the worms rotative axis is greater than that of the portion closer to the rotative axis engaging the balls centrally of the worm. Consequently the worm groove portions near each end must slide on the balls engaged with a gear groove or rotate them faster, while the balls centrally of the worm in contact with the gear will slide on the worm groove or rotate more slowly than the outer balls. Sliding friction will therefore occur between the central or the outer balls and the worm groove,

or between the central and .outer balls rotating at different speeds, or more than one of these 16 Claims. (o1. 74-458) conditions will be present each to a lesser degree. The resultant effect, however, is virtually the same amount of sliding friction between the parts. Such friction also tends to crowd together the balls moving toward the worm center and to spread apart the balls moving away from the worm center, which also increases the friction.

When a cylindrical worm, as shown in Figure 8 of my prior application, is used, onlya single' row of balls is in contact between the worm and Worm wheel at any given instant, so that the unequal and antagonistic movement of balls engaging different gear grooves, as described above, does not occur. In this instance, however, since the periphery of the Worm is notexactly complemental to the periphery of the worm engaged between the worm and Worm gear are I spaced appreciably from either side of this plane they do not fit closely in the groove of either element, because the bottoms of such grooves are.

spaced farther apart than are the bottoms of such grooves in such axial plane of the gear. Consequently the play or backlash between the worm and gear becomes progressively greater as the load carrying balls move farther away from such plane.

It is therefore the principal object of my present invention to provide a worm and gear ar rangement in which only a single row of load transmitting balls is interengaged between such members at any given time, so that no sliding friction will be created either between any balls and the Worm grooves, or between different balls because of their rotation at different speeds, nor will any resistance to movement of balls toward the worm center occur. Since there will be several balls in such single row interengaged between the worm and worm gear members it is necessary, in order to eliminate all sliding friction between these balls, to provide alternate" be such that at least two load carrying balls will be engaged with a single groove of the'worm at all times. I

Another object of my invention is to maintain a close fit of the load carrying balls with both .maintain a close fit of the balls in the worm and worm wheel grooves, and plieferably actually.de-

creases.

More specifically it is an object of m invention to incorporate such worm and gear mechanism in an automotive steering gearffor which applica tion it is important that there be no backlashb'etween the steering column, on which the worm is mounted, and that portion of the steering apparatus'towhich the nor gearsector qr quadrant is connected. Otherwise undesired looseness of the whl'mounting 'mayoccurl ,At the same time it is de s irabletthatlthe efficicncy of such .mechanismib e as high asposs'ibleto reduce the turning effort which must be exerted by the driver on the steering wheel, especiallyin installations for large trucks and ,bus'ses. A

To utilize my novel worm an dgear mechanism most effectively it"is a further object to enable the relationsmpbrme worm and worm gear sector't'o'be adjusted re'latively'within close limits, so that'the proper clearance between the bottoms of thefworm'and gear sectorgrooves may be established, and .maintainedeven' though the parts may become Worn" to a greater or" lesser degree.

In fact, to insure that no play yvilloccur'between the bearing balls and either member engagedtherbyLit is'ah objector my invention to gripthe'loallsbetween such members by resilient pressure thereof toward each other','when desired, The degree of such resilient pressure maybe reg ulated as required.

in the grooves of a worm and worm gear is much more pronounced where the worm gear is relatively small, its radius being not appreciably greater than that of the worm, and perhaps even being less, as in the automotive steering gear assembly illustrated. The reason .ior this is that the gear travelsthroughwsuch a large angle each time the worm makes a complete revolution. In the typical instance selected the gear moves 20 degrees for each revolution of the worm. The pitch of aworm helix is slight, and consequently the distance between allportions of any given worm'gear groove and the axis of the worm is nearly un-itorm if the worm gear periphery has the proper concavity axially to embrace the .worm, as is customary. The average spacing between the Worms axis and the bottom of a worm gear groove through which that axial plane of 'the worm gear perpendicular to the worm rotative axis passes, and'the average spacing .between the worms axisand the .bottom of .agear groove spaced 10 degrees .fromsuch groove, however, are appreciably different. Whileall the balls in any single groove, whicharelof the-same size, will bear substantially vequally against both the worm and gear, therefore, whether the Worm is of the cylindrical type or is concave axially, .the balls in gear grooves spaced apart a substantial angle, for example 10 degrees, will not bear simi- Additional features of my invention, and more particularly ofmy preferred structureintended forusein automotive steeringgears, will'be 'men tioned'in the following detailed description of the embodiment illustrated in the accompanying drawings. Various changes may, of course, be made in the construction within the scope of my invention as defined in the appended claims, and it maybefincorporated in worm and'gear mecha nisms for other uses than in steering gears.

Figure l is a sectional view through .an auto motive steering gear assembly in which the worm is in elevation. 'Figure 2 is a sectional view through the same ,mechan'ismtaken perpendicu;

larly to' the section of Figure .1 and showing in elevationthe-shaft carrying the worm gear.

Figure 3 is a transverse sectional vieWthroujg'h worm and worm gear sector mechanism similar to Figure 2, but showing parts broken away and illustrating a modified'form of mounting. Figure 4.-'is a sectional view through'the same device taken on line 44 or Figure 3. a g

Figure :5 is a fragmentary sectional" view 7 "through a worm of the'type shown in Figures 1, 2 and 13., provided with a difierenttype of by-pass passage through the worm.

Figure 6 is a graph illustrating, 'ona greatly enlarged scale, the developed contour'of the worm groove with relation to the worms rotativelaxis measured in degrees of worm and wormgear'rotation. The problem of maintaining a close fit of "balls particular instance the gear sector groove thus located happens to be its central groove, but it is immaterial which one of its grooves is thus disposed as'far as the engagement-of balls I0 is concerned. "With the worm and gear .in this particular relationship-they may be spaced so that the load carrying 'balls'bear'properly and without apprecia'ble backlashin thegrooves of both elements regardless of the contour of the worm. .Myiinven tion enables such engagement in the .groovesof both thegear and worm to be preserved in aurotative positions of the worm.

It 'willbe understood, of course, that'when alternate large and small balls are employed, as taught in my aforementioned Patent- 'No. 2,298,011, which is preferred, onlyithe larger or load carrying halls will "be thus engaged. As shown inFigure 2, however, the ball size and worm gear widthshouldberelated so 'thatat least two of such larger 'balls will always contact the worm gear groove, to provide proper distribution of the load. 7

As the worm'l is rotated about its axis the worm gear sec'tor'2 will be rotated througha'comparagiven gear sector groove and of the adjacentportion of the worm groove would increase as -.'the gear sector rotated in either direction Ifrom the centered position of ,one io'fjits'ball engaging intersects or substantially coincides with the axial plane of the gear sector which is perpendicular to theaxis of worm I.

As the worm, continued to rotate for swinging the sector in the direction indicated by the arrow in Figure 1, for example, this distance would increase until the worm had rotated through substantially 180 degrees. At that time the load would be transferred from the balls at the left in Figure 1 to the balls at the right, so that the forces between the parts previously transmitted through the central grooveof the gear sector would then-be transmitted through the groove next onthe right ofsuch central groove. The bottomof this groove, as rotation of the, parts in the same direction continued. would approach the worm axis until such groove reached the position of the central worm groove shown in Fig.1.

The spacing between the bottoms of the worm and gear grooves would not changegreatly. during swinging of a gear sector groovethrough degrees either side of its central position, but the variation would be sufficient to permit play in the parts, even though there was no play when the .worm gear groovewas centered relative to the worm To eliminate this play as the worm and gear sector rotate conjointly, the contour of the worm groove bottom may be shaped so that the spacing between the bottom of the ball receiving gear sector groove and the bottom of the worm groove portion adjacent thereto will remain constant during rotation of the gear through an angle of degrees, corresponding to a complete revolution of the worm, provided that such gear angle is substantiallybisected by the axial plane of the gear perpendicular to the worm axis. This result is accomplished by forming the worrngroove of decreasing depth, or increasing the spacing between the bottom of the worm groove and the worms axis, each side of the central portion of the worm,'namely, that portion which is intersected by the axial plane of the gear sector perpendicular to the worms axis. The rate at' which the groove depth decreasesor groove bottom spacing increases is not uniform, but on the contrary, such spacing is found to in: crease almost exactly in proportion to the square of the gear segments angle of rotation for small angles.

For any given angle of worm gear movement the bottom of one of its grooves in the central position of closest approach :to the worm recedes from the Worms axis a distance equal to the difference between the root radius of the gear sector and such radius multiplied by the cosine o f such given angle through which the gear sector is rotated. To find the root radius of the worm at any point this relationship may be written mathematically as follows:

Y--K=R-R cos a=R(1--cos a.)

where Y is the root radius of the worm, K is the minimum root radius of the worm located in the axial plane of the worm gear perpendicular to the worms axis,

R is the root radius of the worm gear, and a is the angle of rotation of the worm gear.

Since for small changes in angle a the change in the factor (l-cos a) is found to be proportional to a (1cos a) =C'a where C is a constant. Forc=1 degree,

so that for other degrees (lcos a)=(1-cos 1*)a Therefore, substituting in the above equation,

YK=R(lcos 1)a2 I Proof that the quantity (l-cos a) varies in proportion to a may be afiorded 'bycomparing calculations of (1-cos 'a) and (1-cos 1)a for angles of worm gear change from 1 degree to 10 degrees. These comparative values are listed in the following table.

(1-005 41) (1cosl)a Worm gear sector degrees This equation is the same form as the equation for a parabola. related to rectangular coordinates as follows:

X =4f(Y-K) Where X and Y are the coordinate values,

f is the distance between the focus and the apex, which is constant for any selected parabola, and I K is the ofiset of the apex from the X axis.

It will be seen by comparing the values of (1- cos a) with those of (1cos 10)a in the above table that for any angular departure from central position of a worm gear groove up to about 7 degrees, the difference between the values YK using (1-005 a) and the equation for a curve of true parabolic shape of developed worm root curve is less than .00001 R. Hence where the worm gear pitch radius is 1 inch the Worm root would conform to true parabolic shape within one one hundred thousandth of an inch for an angular worm gear movement of 7 degrees. Even for an angular gear. movement of 10 degrees the difference in such calculations is only about .00004 of an inch, which is negligible. Consequently we may assume that if the developed curve of the worm groove bottom is of parabolic shape, for small angles of worm ear movement the spacing between the bottoms of the worm gear groove and the adjacent portion of the worm groove will remain constant. i

If, on the other hand, the bottom of the worm groove, when developed, were merely a straight line, as in a conventional cylindrical worm, instead of a parabolic curve, the worm gear groove bottom would have receded from the bottom of the worm groove a distance of .01523 of an inch, or approximately of an inch, if the root diameter of the worm were one inch, during a. 10' degree angular movement ,of the worm gear groove from its central location of closest approach to the worm axis. This variation would which my invention eliminates.

..cause sliding Jfriction, occurs.

s or er-s In Figure 6 of the drawings the-nevelopedzcontour of the .parabolic-wormggroove bottom is shown on a greatly exaggerated scale. In determining this developed 'shape -of the worm groove bottom-iei-ther oneofgtheiollowing equations maybe used at the will of the designer:

In applying either of these formulas 'it-wil-l be understood 'that'the maximum value of the gear sector angle a will be that through which such gear. sector is moved by one-half a revolution of the worm. 'This'is necessary so that only one gear groove will be engagedby balls at any fgiven time-except perhaps for a brief instant du'ring'which balls are being disengaged from 'one wormgear grooveandengaged with an adjacent groove. Duringsuch transition, however, the balls in the two gear grooves will engage worm portions of equal radii, so that no "resistance to movement of the balls, tending to The maximum value of worm gear angle a will, of course, depend upon the pitch =of theworm grooveandfthe worm gear radius.

For angles of worm gear movement a greater than that corresponding to a 180 degree rotation of the Worm the value of Y must be less than that which Wouldfbe obtained by 'a solution of either of the equations above, so that the balls will be released abruptly from the gear groove moving away from'a position centrally of the wormlas the balls .eng age in the adjacent gear groove moving toward said position. Although Y might still continue to increase beyond 180 de-' grees'from the worm center, the rate of increase must be .more gradual than that governed by the above equations; but it 'ispre'ferred thatbeyond such worm 'a'ngle the value of Yiactually decrease. The further alternative is forY toremain constant above the worm angle of -180 degrees -irom center. For iconvenience the rate of ':Y-.decrease 7 may bet-he same as its previous rate-of increa'se,

so that 'either'of the same equations couldbe sed by substituting decreasing angles of. az'beyond .10 degrees. The sections .of the developed "Worm curve at oppo'site sides of each 180degreezsection thus join to form substantialiy a ceratoid -.=cusp;.

This .conformation is shown in:the;curve of Fig. i6,

and't-he worm groove may-be .ground'in this-fashion by shifting e, grinding wheel towardand away from the wormlaxis :under the control :xof a'camof proper contour. "This worm construction insures that the load will beitransmit-ted between the worm and worm .gear elements .by balls in :only a single wormsgear groove. atiany given time,with'the'negligibleexception of the instant the load is -being transferred ;;from :the balls in one worm gear groove 'tothe balls in an adjacent groove.

As an example. ofaa installation slt;has

been-stated that thefworm gearxigma'y be rotated 8 torzgrooves are providedat each side di its nentrail-groove. .During-one -complete' revolution of the worm from the position 's'hown in i-F igm e' l it will :retur-n-Lto the identical-position, out the balls 1 will engage t'he worm --gear g-roove adiathe other hearing l 1 "is held= in place by acover #3 boltecl -to'the-casing. The-shaft fl-carrying the worm I extends through a bore I'=5- in the casing, so that its-criterend is accessible *for rotating the worm. This shaft may constitute the steering column of an automotive vehicle.

The worm 'gear sector 2 is mounted ona shaft 22, which may be'supported byspaced fantiiric tion bearings 23 oftheneedlefbeafingiype. The outer end 24 of this shaft may be spiined and threaded for attachment to *a-steer'ing am.- A cover 25 bolted to thepasing 1H removable for accessto thewormegearsector. The worm bearings -H and l'lwvil-l be'located so that the central plane "through the worm'fi, perpendicular to shaft ll,--cdincides with theaxis of the gear sec-tor shaft 2 2. A =-smail variation inthe location 0f such plane axially of the'worm distance between their axes.

Bea-rings 23-may be received in "a sleeve 26 fitting closely ina-borein "casing'fZ'I and rotatable relative tO'j-t. If these-hearingsare'locate'd slight-1y -eccentrica lly of the axis 'ojf the cylindrical exterior [of 1 this sleeve, "the ails er shaft 2 2 may 1 bemoved slightly; toward'or away "from the casing. The spacingbetweentheaxes ofthe sleeves inner .andfiaouteryperipheriesmay be of the order of one sixty-fourth of an inch. The desired spacing between the axes of the worm l and gear 2 maytherefore"abetestabishedneither initially or \after 'ithe: igiZQOME-ls. in the worm and worm :gear sector have abecume somewhat :morn, merely by setting such sieeveiin corresponding rotative .position. The. ssleeveunay; then he held. inwsuch setting :by :a I set :screw '22:! rzthrieaded in the wall of-casing .2] and having-an inner tip adapted to press againstthesleeve .or'tdfit in any one of a number of'hdles disposedcircumferentially arounduit, Such holes 28 are shown in Figure 4, disclosing a structure slightly different frOm that' of-FigL-QI T The modification. of FiguresB and 4 also incorporates a'sleeve 26 having a slightly eccentric bore, and which fits closely within casing 2|. In this instance, however, the bearings 23 do not seat directly upon the inner periphery of the sleeve 26. On the contrary, a resilient bushing 29 of rubber, or preferably of similar synthetic material, is interposed between the sleeve 26 and an inner tube 26' which retains the bearings. The rubber bushing should be suitably bonded to both of these'parts so that the composite resillent unit can be rotated to adjust the position of the gear sector shaft axis toward or away from the axis of worm I.

Since sleeve 26 is of varying wall thickness the axis of gear shaft 22 will be closest to the axis of worm I when the thickest part of the sleeve is located farthest from the worm and immediately beneath locking screw 21, as shown in Figure 4. If the balls are engaged fairly tightly between the worm and the worm gear sector when theparts are in the relative positions of Fig. 1, rotation of sleeve 26 to locate a thicker wall portion beneath the locking screw would compress the side of resilient bushing 29 remote from the worm radially between sleeve 26 and tube 26'. The balls III would then be clamped between the worm, and worm sector under resilient pressure, which may be varied in degree by proper rotative'adjustment of sleeve 26.

Where a two-part sleeve for carrying bearings '23 is used, as shown in Fig. 3, sleeve 26 may be turned sufliciently so that, when a gear sector groove is located centrally of the worm, the bush-. ing 29 will be compressed to a substantial de ree. All backlash between the worm and the worm gear sector will be eliminated by this expedient when the parts are in the relationship of Figure 1, yet the friction of the mechanism will not be increased appreciably because, as mentioned previously, the use of alternate large and small balls eliminates all sliding friction between adjacent balls, provided that they all rotate at the same peripheral speed.

' As worm I is now turned the pressure of the compressed bushing 29 will continually urge worm gear shaft 22 toward the worm axis to prevent backlash in all rotative position of the worm. Moreover, when the spacing between the bottoms of the worm gear groove engaged by the balls and of the worm groove is kept constant by use of the structure described above, the resilient pressure of the worm and worm gear sector against the balls will remain constant. If the worm is of conventional cylindrical type, however, such pressure .will vary somewhat as bushing 29 expands to move gear shaft 22 toward the worm to compensate for the tendency of the spacing between the bottoms of the gears ball engaging groove and of the cooperating portion of the worm grooveto increase. v

To permit such movement of the gear sector the sum of the lengths of themaximum worm and gear radii must. be less than the perpendicular distance betweentheir axes, so that the point of the gear periphery closest to the worm will not come ifito engagement with it. Even though the worm is of the cylindrical type, therefore, having a constant root diameter, and although the pressure on the bearing" balls It! may vary, the resilient worm gear mounting can cause the worm and gear to exert suflicient pressure upon such balls in all rotative positions of the Worm to prevent'appreci able backlash between the parts. I The variation in pressure on the balls insuch anassemblywill not vary too greatly because the maximum variation in the distance between the bottom of a groove of a fixed gearsector and the axis of the worm during rotation of the worm through 180 degrees would be only about /64 of an inch in a typical instance. The variation is nevertheless suflicientlylarge to'permit undesirable backlash if no compensation is provided.

Since it is desirable to lubricate needle bearings 23, as well as the worm and gear, for example through lubrication fittings 3 of conventional type shown in Fig. 1, it is preferred that the resilient bushing 29 be of material not deteriorated by petroleum'products. Reference to such bushing as of rubber, therefore, is intended to include synthetic rubbers such as Neoprene and other resilient lubricant resistant substances suit able for the purpose described. 7 As in the worm and gear mechanism shown in my previous pplication Serial No. 517,927, the balls circulate through a by-pass aperture IS in the worm body extending between the ends of the effective portion of the worm groove, which is preferably about oneand one-half turns. The balls are guided for movement through passage l6 by suitable deflectors shown in Figure 1. Also the balls may be held more closely in the groove to prevent variation in clearance between the balls by forming the casing of a contour complemental to the variation in groove depth. 1Thus the casing may have a hump or ridge located centrally of the worm, as shown exaggerated in size in Fig. 1. Since the difference in spacing between the worms axis and the bottoms of extreme portions of the groove is so slight, however, thisexpedient may not be necessary.

Where antifriction mechanism of scribed is incorporated in an automotive steering gear it is usually desirable for the steering column M to be tubular so that electrical wires may pass through its hollow interior l1. In such event an aperture 18, as shown in Fig. 5, may extend axially through the worm I. Such an, aperture would conflict with a ball by-pass passage such as 16 in Fig. 2, which is disposed in a diametral plane of the worm. The balls may, however, pass between the same portions of the worm groove through the passage l9v of Fig. 5, composed of end portions meeting at an angle. Alternatively a linear by-pass passage may be located, in a chordal plane at one side or the other of the axial aperture I8, instead of in a diametral plane as shown in Fig. 2.

I claim as my invention: V 1. Antifriction worm and gear mechanism, comprising a gear having an inclined groove therein, a worm adjacent to said gear and having only a single helical groove therein complemental to the inclined groove of said gear, th spacing of the bottom of the worm groove from the worm axis being minimum substantially in an axial plane of said gear disposed perpendicular to the axis of said worm,vand such spacing between the worm groove bottom and the .worm axis increasing progressively away from such plane throughout a distance to each side of such planenot appreciably exceeding one-half a turn of the Worm groove, and balls engaged closely by the grooves of said gear and worm. v

2. Antifriction worm and gear mechanism, comprising a gear having an inclined groove therein, a worm adjacent to said gear and hav ing only aisingle helical groove therein complemental' to the inclined groove of said gear,'the spacing of the bottom of the worm' groove from the type de- -a i lplane of said gear. disposed .perpendicue Iar. tothe axis ofjsaid.worm,, and such spacingbetween. the wormgroove bottomand th worm. axis increasing progressively, substantially inpro- 1 portion to the root radiuseo-f said gear minus. "the cosine of. the gear angle. multiplied by the gears root radius, awayv from such. plane 1 throughout a distance toeachuside ofsuch..plane not appreciably exceeding one-half a. turn of theworm groove, and balls. engaged, closely by V the. grooves. of. said gear and WornL .3. Antifriction worm and gear mechanism,

an axial plane of said gear; disposed perpendicu- 12 therein, a worm adjacent to said gear and having. only a single. helical; groovethereimcomplemental. to. the; inclined groove. of said gear, bottom: of the worm groove as developedon aplane being, of. substantially parabolically concave contour axially of said. worm throughoutadistance lar to the axislof said. worm-,,and.such. spacing. between the Wormgroove bottom and. the; worm axis. increasing, progressively away from, such 7 side of 'such plane not. appreciably exceedingonehalf. a turn of theworm groove, andballs enga ed closely by the grooves of. said. gear. andworm.

4. 'Antif'riction worm. and. gear. mechanism,

A comprising, a gear having. an. inclined groove therein,' a worm. adjacentzto said gear and hav ing. only a. sing1e. helical. groove. therein complej mentalgto theihclinedigroove ofsaid gear, the.

spacing of the bottom of. the worm groove from the worm axis. being. minimum substantially in 1 an axial plane of said; gear disposed perpendicular. tothe axis of. said? worm, .and. suchspacing between the wormgroove bottom and. the worm axis'increasing progressively away from. such planethroughout adistanceto eachside of such planenot appreciably exceeding one-half-a turn ofithe, worm groove,: and balls. engaged, closely by. the groovesgof. said gear. and. worm, the spacing. between the. worm groove bottomand the 1 worm. axis. decreasing progressively immediately beyond. eachsuch. half. turn of. the. worm to. re: 1ease..the..bal1s abruptlyfrom close engagement with said gear. and worm grooves.

5.. Antifri'ction wormand'gear. mechanism comprising. a gear having. 1 an. inclined groove there.- in,..a worm adjacent tosaid gear and. having a helical.- groove therein, complemental to. the in.-

clined' groove of said ear, the worm. groove. as

developed on a planebeing. concaveaxially. of i said, worm. throughout approximately. one compljete turn, andLa, portion. of the developed worm groove joiningan endjof said concave portion. in a, crest,,and balls engagedlcl'osely by the groove ofisaidgear and by such concave portion of the worm groove. as developed.

6'. Antifri0tion worm and gear mechanism cominclined groove asdevel'opedon a plane being concave axially of said, Worm throughout approximately one comj pl'ete turn, and" a portion of.- the dev'elopedworm groove adjoining an'end" of 'said" concave portion 1 being similarly concave and joinin such first cncave portion. in a crest, and balls. engaged closely by the g rooveof saidgearand such. first concave portion oi'thewormgroove asdeveloped not. appreciably exceeding a. complete turn, and balls engaged closely by the. groove offsaid gear. and the parabolic portionot the Worm groove as developed, r 7

8.. Antifriction worm and; gear mechanism, comprising a gear having an. inclined groove. therein, a worm adjacent to said gear and-thaving a. helicalgroove. therein complemental toQt-he inclined. groove. of rsaidz-gear, the bottom of: the worm groove as. developed on. a plane being-of substantially parabolically concave contour axial?- ly of said. worm. throughout approximately a. com-- plete turn, a. portion oi the developed. worm roove. adjoining .an.end of such parabolic por tion. departing substantially from. a. continuation.

of suchrparabolically concave. contour; and balls:-

engaged closely by the groove-oi said. gear and. the parabolic portion. oil the. worm groove. as developed. v 1' J 9. Antifriction worm: and. gear mechanism; comprising a gear having an. inclined groove therein a worm adj acent said gear andhavingra. helical 'gro'oveltherein complementalto the in-.- clined. groove ofsaid gear, the bottom of the worm groove as developed. on. a. plane. being. of substantially parabolically concave. contour axially. of.

said. worm. throughout. approximately a. complete turn,.a portion. of. the developedgworm groovead; joining an end. of such. parabolic. portion being of reverse...curvature,. and .ballsengaged closely by the; groove of. said. gear and. the. parabolic portion of. the Worm groove as. developed,

10.. Antifriction worm and gear mechanism comprisinga gear having} an. inclined groove therein, a worm adjacent. to sai'dgear and having. a. helical groove, therein .complemental to the. in-fl. clined groove of. said; gear, balls engagedjbetween the groove of said gear and the wormgroove,.and means supporting. said. wormandlgear. andlresiliently urging them relatively toward eachlother to clamp sai'dballs under resilient pressure. between. such gear. and worm grooves in all' rotative positionsof the worm andgear.

11; Antifriction worm and gear. mechanism. comprising a gear having an inclined groove therein, a worm adjacent to said. gear and'having, a. helical. groove therein..complemental'to. theinclined. groove of said. gear, ballsen'gagedl'between the groove of. said gear. and the worm groove, two shafts, one. supporting said worm and the other. supportingsaid gear, adjusting means includinga. sleeve of varying wall. thickness encircling, one of said shafts: and circumferentially' adjustable to varythe position of such shaft toward or: away from the other shaft; toadjust the engagement of said balls by such gear and wormxgroovesiin all rotative positions of thezworm and gear a tube interposed between said sleeve, and the shaftencircled thereby, and a resilient bushing inter posedbetween' saidtube" and said sleeve, adapted to be deformed, by circumferential adjustmentiof said sleeve tendingto effect approach movement of. said shafts; and. thereby resiliently urging them relatively toward each othert'o: clamp, said 1 b'allsunderresilient pressure;

'7. Antif'riction Worm. and. gear mechanism,.

1'2; Antifriction worm and gear mechanism; comprising a gear having. an inclined groove therein, a'worm' adjacentto said gear ancl'having only a single helical groovetherein complement'a'l.

to the inclined groove of said gear, balls engaged between the .groove of said gear and the worm groove, and means supporting said worm and gear and urging them relatively toward each other to clamp said balls under resilient pressure between such gear and worm grooves, the pacing of the bottom of the worm groove from the worm axis being minimum substantially in an axial plane of said gear disposed perpendicularly relative to the axis of said worm, and said spacing between the worm groove bottom and the worm axis increasing progressively away from such plane throughout a distance to each side of such plane not appreciably exceeding one-half a turn of the worm groove, and sufliciently to maintain the spacing between the bottom of the gear groove and the bottom of the worm groove substantially constant throughout a complete turn of the worm, thereby to maintain substantially constant the resilient pressure of said supporting means on said balls in all rotative position of the worm and gear.

13. Antifriction worm and gear mechanism, comprising a gear having an inclined groove therein, a worm adjacent to said gear and having only a single helical groove therein complemental to the inclined groove of said gear, balls engaged between the groove of said gear and the worm groove, two shafts, one supporting said worm and the other supporting said gear, and adjusting means including a sleeve of varying wall thickness encircling said gear supporting shaft and circumferentially adjustable to vary the position of such shaft toward or away from said worm supporting shaft, to adjust the engagement of said balls by said gear and worm grooves, the spacing of the bottom of the worm groove from the worm axis being minimum substantially in an axial plane of said gear disposed perpendicularly relative to the axis of said worm, and said spacing between the worm groove bottom and the worm axis increasing progressively away from such plane throughout a distance to each side of such plane not appreciably exceeding one-half a turn of the worm groove, and sufficiently to maintain the spacing between the bottom of the gear groove and the bottom of the worm groove substantially constant throughout a complete turn of the worm, thereby to maintain substantially constant the adjusted engagement of said gear and worm grooves on said balls in all rotative positions of the Worm and gear.

14. Antifriction worm and gear mechanism, comprising a gear having an inclined groove therein, a worm adjacent to said gear and having only a single helical groove therein complemental to the inclined groove of said gear, balls engaged between the groove of said gear and the worm groove, two shafts, one supporting said worm and the other supporting said gear, adjusting means including a sleeve of varying wall thickness encircling said gear supporting shaft and circumferentially adjustable to vary the position of such shaft toward or away from said worm supporting shaft, a tube interposed between said sleeve and said gear shaft, and a resilient bushing interposed between said sleeve and said tube, and compressible by circumferential adjustment of said sleeve to press said gear resiliently against said balls, the worm groove developed on a plane being concave axially of said worm throughout approximately one complete turn to maintain the spacing between the bottoms of the gear groove and of such portion of the worm groove substantially constant, so that the resilient pressure of said gear on the balls effected by said bushing remains substantially constant in all rotative positions of the worm and gear.

15. Antifriction worm and gear mechanism, comprising a gear having an inclined groove therein, a worm adjacent to said gear and having a helical groove therein complemental to the inclined groove of said gear, the worm groove as developed on a plane being concave axially of said worm throughout its central portion, and a portion of the worm groove, in its developed form, joining an end of said concave portion to form therewith substantially a ceratoid cusp, and balls engaged closely by the groove of said gear and by such portion of the worm groove concave in its developed form.

16, Antifriction worm and gear mechanism, comprising a gear having an inclined groove therein, a worm adjacent to said gear and having a helical groove therein complemental to themclined groove of said gear, balls engaged between the groove of said gear and the worm groove, two shafts one supporting said worm and the other supporting said gear, a sleeve encircling one of said shafts, a tube interposed between said sleeve and the shaft encircled thereby, bearing means interposed between said tube and said shaft, and a resilient bushinginterposed between said tube and said sleeve adapted to be stressed to urge said tube therewithin in a direction to press said gear and worm resiliently toward each other to clamp said balls under resilient pressure.

HENRY S. HOFFAR. 

